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Make 9


Alignments to Content Standards: K.OA.A.3

Task

Make 9 in as many ways as you can by adding two numbers between 0 and 9.

IM Commentary

Because of the limited reading skills of kindergarten students, this task should be introduced by the teacher, followed by the students carrying out the activity. Teachers should have counters on hand for students to use.

There are two other tasks that are very similar to this but which have contexts. As with several other tasks in the set, any number between 2 and 10 can be used in place of 9 to address K.OA.3.

Although not necessary to meet this standard, listing the possible pairs of numbers in a systematic way might help the student show that s/he has found all of the possible number pairs that make 9.

The Standards for Mathematical Practice focus on the nature of the learning experiences by attending to the thinking processes and habits of mind that students need to develop in order to attain a deep and flexible understanding of mathematics. Certain tasks lend themselves to the demonstration of specific practices by students. The practices that are observable during exploration of a task depend on how instruction unfolds in the classroom. While it is possible that tasks may be connected to several practices, only one practice connection will be discussed in depth. Possible secondary practice connections may be discussed but not in the same degree of detail.

This particular task helps illustrate Mathematical Practice Standard 7, Look for and make use of structure. Kindergartners are introduced to an exploration that builds the underpinnings of understanding the commutative property. MP. 7 emphasizes the importance of students recognizing relationships and making connections between different ideas. In this case, students observe that when they tried to find all the sums of 9 they could add the same 2 addends but in a different order.  This eventually leads to recognizing that the structure of the commutative property basically cuts their learning of addition facts in half.

Solution

Students may use objects or drawings to find the decompositions and then should record each decomposition by drawing pictures or writing equations. Students should include two or more of the following possible decompositions. Note that the “9” may appear on either side of the equal sign.

Possible equations:
0+9 = 9; 1+8 = 9; 2+7 = 9; 3+6 = 9; 4+5 = 9;
5+4 = 9; 6+3 = 9; 7+2 = 9; 8+1 = 9; 9+0 = 9

Lisa says:

over 1 year

The standard says to decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings and record each decomposition by a drawing or equation.

What does the "more than one way" refer to... decompose more than one way (i.e. 10 = 0 + 10, 10 = 9+ 1, 8 + 2 = 10, 3 + 7 = 10, 10 = 4 + 6, 5 + 5 = 10) or does it refer to their ability to show it more than one way with objects, drawing, and an equation?

In other task commentary it said that the commutative property was not necessary to meet the standard, but is it necessary that students list ALL combinations to meet the standard?

For example, with 10; is it necessary to list all of these: 1 + 9 or 9 + 1 2 + 8 or 8 + 2 7 + 3 or 3 + 7 6 + 4 or 4 + 6 5 + 5 in order to consider meeting the standard?

Or if students list just 9 + 1 and 8 + 2 is that considered meeting?

Bill says:

over 1 year

It means the first, that is different additions, not different representations. And no, I would not say that listing all the ways is a requirement of the standard, although if the student just listed 9 + 1 and 8 + 2 I would expect a response to the question "can you think of any more?"